Numerical Analysis of Fully Discretized Crank–Nicolson Scheme for Fractional-in-Space Allen–Cahn Equations
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Title
Numerical Analysis of Fully Discretized Crank–Nicolson Scheme for Fractional-in-Space Allen–Cahn Equations
Authors
Keywords
Fractional derivatives, Allen–Cahn equations, Finite difference method, Maximum principle, Energy stability, Error analysis, 65M70, 65R20
Journal
JOURNAL OF SCIENTIFIC COMPUTING
Volume 72, Issue 3, Pages 1214-1231
Publisher
Springer Nature
Online
2017-02-25
DOI
10.1007/s10915-017-0396-9
References
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Note: Only part of the references are listed.- On the maximum principle preserving schemes for the generalized Allen–Cahn equation
- (2016) Jie Shen et al. Communications in Mathematical Sciences
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- Nonlinear stability of the implicit-explicit methods for the Allen-Cahn equation
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- Stabilized Crank-Nicolson/Adams-Bashforth Schemes for Phase Field Models
- (2013) Xinlong Feng et al. East Asian Journal on Applied Mathematics
- Phase-Field Models for Multi-Component Fluid Flows
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- An unconditionally gradient stable numerical method for solving the Allen–Cahn equation
- (2009) Jeong-Whan Choi et al. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
- A Space-Time Spectral Method for the Time Fractional Diffusion Equation
- (2009) Xianjuan Li et al. SIAM JOURNAL ON NUMERICAL ANALYSIS
- Numerical Methods for the Variable-Order Fractional Advection-Diffusion Equation with a Nonlinear Source Term
- (2009) P. Zhuang et al. SIAM JOURNAL ON NUMERICAL ANALYSIS
- Numerical Studies of Discrete Approximations to the Allen–Cahn Equation in the Sharp Interface Limit
- (2009) Jian Zhang et al. SIAM JOURNAL ON SCIENTIFIC COMPUTING
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